<h2>Introduction</h2>

The following table shows benchmarking results of various tests for the available prover engines in GeoGebra:

<ul>
<li>Column "Engine 1" refers to <a href="http://ggb1.idm.jku.at/~kovzol/papers/Kovacs-Recio-Weitzhofer-20120323.pdf">Recio's exact check method</a>
programmed by Weitzhofer.
<li>Column "Engine 2" refers to <a href="http://ggb1.idm.jku.at/~kovzol/papers/Botana-Kovacs-Weitzhofer-20120326.pdf">the Groebner basis method
via SingularWS (also known as Botana's method)</a> programmed by Kovacs.
<li>Column "Engine 2, Giac" refers to <a href="http://ggb1.idm.jku.at/~kovzol/talks/ricam3/Parisse-Kovacs.pdf">the
Groebner basis method via the Giac computer algebra tool</a> (instead of SingularWS) programmed by Parisse and Kovacs.
<li>Column "Engine 3a" refers to <a href="https://code.google.com/p/open-geo-prover/">OpenGeoProver's</a>
<a href="http://en.wikipedia.org/wiki/Wu's_method_of_characteristic_set">Wu's method</a> implementation programmed by
Petrovic and Janicic.
<li>Column "Engine 3b" refers to OpenGeoProver's <a href="http://www.eleves.ens.fr/home/desfonta/InternshipReport.pdf">Area method</a>
programmed by Desfontaines.
<li>The Auto approach
refers to the automatic selection of methods which is already
implemented in GeoGebra and it usually starts with "Engine 1" and
then it continues with "Engine 2" (either via SingularWS or
Giac: if SingularWS is available, then in SingularWS, otherwise in Giac). If
the Groebner basis method is not conclusive, then "Engine 3a" is tried.
If it is not conclusive either, then OpenGeoProver's
Area method (Engine 3b) is used.</p>
</ul>

Explanation of the used colors:

<ul>
<li>Green means that the test returns a correct yes/no answer. Intensity of green
means speed (the lighter the slower). Numbers are in milliseconds.
<li>Pink means that GeoGebra returns the wrong answer.
<li>Yellow means the output is not conclusive, thus using this method
GeoGebra shows "undefined", i.e. there is no error here.
<li>The Result column provides some extra information about the result, such as
"false" when the statement was false on purpose.
</ul>

<p>The Speed column shows the timing. Highlighted entries are the best results.</p>

The <a href="http://dev.geogebra.org/trac/browser/trunk/geogebra/test/scripts/benchmark/prover/tests/">test cases</a>
are also available for download in GeoGebra's .ggb format from the GeoGebra online source code directly.
